How to find the mean and standard deviations from the below control chart and calculate defect rate
Subgroup | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
1 | 3.757 | 3.753 | 3.744 | 3.755 | 3.757 | 3.741 | 3.746 | 3.746 | 3.760 | 3.741 | 3.749 | 3.746 | 3.743 | 3.755 | 3.745 | 3.748 | 3.757 | 3.740 | 3.756 | 3.742 | 3.752 | 3.746 | 3.745 | 3.752 |
2 | 3.749 | 3.739 | 3.745 | 3.753 | 3.760 | 3.749 | 3.743 | 3.753 | 3.755 | 3.745 | 3.751 | 3.749 | 3.751 | 3.744 | 3.751 | 3.746 | 3.747 | 3.739 | 3.757 | 3.753 | 3.751 | 3.753 | 3.762 | 3.755 |
3 | 3.751 | 3.747 | 3.740 | 3.753 | 3.751 | 3.745 | 3.753 | 3.747 | 3.757 | 3.751 | 3.757 | 3.744 | 3.745 | 3.753 | 3.747 | 3.755 | 3.756 | 3.752 | 3.749 | 3.754 | 3.749 | 3.741 | 3.753 | 3.753 |
4 | 3.755 | 3.751 | 3.741 | 3.749 | 3.754 | 3.742 | 3.751 | 3.755 | 3.757 | 3.741 | 3.754 | 3.757 | 3.739 | 3.755 | 3.751 | 3.755 | 3.759 | 3.744 | 3.755 | 3.743 | 3.753 | 3.746 | 3.750 | 3.749 |
5 | 3.749 | 3.751 | 3.742 | 3.739 | 3.750 | 3.743 | 3.747 | 3.758 | 3.749 | 3.740 | 3.755 | 3.737 | 3.750 | 3.754 | 3.744 | 3.749 | 3.751 | 3.745 | 3.744 | 3.741 | 3.755 | 3.743 | 3.744 | 3.754 |
6 | 3.759 | 3.744 | 3.743 | 3.747 | 3.753 | 3.742 | 3.751 | 3.756 | 3.741 | 3.741 | 3.753 | 3.749 | 3.747 | 3.766 | 3.745 | 3.749 | 3.756 | 3.757 | 3.741 | 3.748 | 3.750 | 3.744 | 3.750 | 3.756 |
n | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
A2 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 | 0.483 |
D3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
D4 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 | 2.004 |
X-bar | 3.753 | 3.748 | 3.743 | 3.749 | 3.754 | 3.744 | 3.749 | 3.753 | 3.753 | 3.743 | 3.753 | 3.747 | 3.746 | 3.755 | 3.747 | 3.750 | 3.754 | 3.746 | 3.750 | 3.747 | 3.752 | 3.746 | 3.751 | 3.753 |
X-bar-bar | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 | 3.749 |
UCL | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 | 3.755 |
LCL | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 | 3.743 |
R | 0.010 | 0.014 | 0.005 | 0.016 | 0.010 | 0.008 | 0.010 | 0.012 | 0.019 | 0.011 | 0.008 | 0.020 | 0.012 | 0.022 | 0.007 | 0.009 | 0.012 | 0.018 | 0.016 | 0.013 | 0.006 | 0.012 | 0.018 | 0.007 |
R-bar | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 | 0.012 |
UCL | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 | 0.025 |
LCL | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Mean | ||||||
Standard Deviation | ||||||
Target | 3.75 | |||||
Tolerance | 0.005 | Lower | Upper | Total | ||
Spec | ||||||
Delta | ||||||
Z | ||||||
P |
How to find the mean and standard deviations from the below control chart and calculate defect...
Please show steps, I need help on understanding how to do. Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a lower class limit of 3.720 in., and use a class width of 0.010 in. 3.749 3.757 3.753 3.726 3.731 3.743 3.744 3.725 3.756 3.757 3.754 3.745 3.745 3.732 3.746 3.754 3.727 3.752 3.744 3.723 3.749 3.765 3.754 3.758 3.758 3.731 3.751 3.761 3.757 3.746